A Note on Stability of Event-Triggered Control Systems with Time Delays

TL;DR

This paper analyzes the stability of event-triggered control systems with time delays, introducing a novel inequality to establish sufficient stability conditions and prevent Zeno behavior, supported by numerical simulations.

Contribution

It develops a new Halanay-type inequality to ensure stability and allows parameter selection to avoid Zeno behavior in event-triggered control systems with delays.

Findings

Established stability conditions for event-triggered systems with delays

Proved that the event-triggering parameter can be freely chosen to prevent Zeno behavior

Validated theoretical results with numerical simulations

Abstract

This note studies stability of event-triggered control systems with the event-triggered control algorithm proposed in [1]. We construct a novel Halanay-type inequality, which is used to show that sufficient conditions of the main results in [1] ensure stability of the event-triggered control systems that was missing in [1]. It is also shown that a positive parameter in the proposed event-triggering condition in [1] can be freely selected to exclude Zeno behavior from the event-triggered control system. An illustrative example is investigated to demonstrate the theoretical results of this study with numerical simulations. [1] K. Zhang, B. Gharesifard, and E. Braverman, Event-triggered control for nonlinear time-delay systems, IEEE Transactions on Automatic Control, vol. 67, no. 2, pp. 1031-1037, 2022.